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JOURNAL OF CLIMATE

VOLUME 22

15SEPTEMBER2009

Changing Frequency and Intensity of Rainfall Extremes over India from 1951 to 2003 CHANDRA KIRAN B. KRISHNAMURTHY School of International and Public Affairs, Columbia University, New York, New York

UPMANU LALL Department of Earth and Environmental

Engineering, Columbia University, New York, New York

HYUN-HAN KWON Water Resources Division, Korea Institute of Construction

Technology, Gyeonggi-do,

South Korea

(Manuscript received 17 October 2008, infinalform 6 February 2009)

ABSTRACT Using a 1951-2003 gridded daily rainfall dataset for India, the authors assess trends in the intensity and frequency of exceedance of thresholds derived from the 90th and the 99th percentile of daily rainfall. A nonparametric method is used to test for monotonic trends at each location. Afieldsignificance test is also applied at the national level to assess whether the individual trends identified could occur by chance in an analysis of the large number of time series analyzed. Statistically significant increasing trends in extremes of rainfall are identified over many parts of India, consistent with the indications from climate change models and the hypothesis that the hydrological cycle will intensify as the planet warms. Specifically, for the exceedance of the 99th percentile of daily rainfall, all locations where a significant increasing trend in frequency of exceedance is identified also exhibit a significant trend in rainfall intensity. However, extreme precipitation frequency over many parts of India also appears to exhibit a decreasing trend, especially for the exceedance of the 90th percentile of daily rainfall. Predominantly increasing trends in the intensity of extreme rainfall are observed for both exceedance thresholds.

1. Introduction Anthropogenic climate change poses potentially sig nificant risks for the Indian Subcontinent through changes in extreme rainfall characteristics. G e n e r a l circulation models ( G C M s ) of climate have had only limited success in reproducing the key attributes of the intraseasonal and interannual variations i n the Indian monsoon. Conse quently, it is not clear whether GCM simulations forced with the Intergovernmental Panel o n Climate Change (IPCC)-style anthropogenic change scenarios adequately represent changes i n Indian rainfall extremes, especially for extreme rainfall that translates into floods or for multiday dry periods that impact crop yield. Recently, a few papers (Guhathakurta and Rajeevan 2008; G o s w a m i

et al. 2006) have investigated the trends in selected ex treme rainfall attributes from a daily rainfall dataset that has become available through the Indian M e t e o rological Department ( I M D ) . Such analyses provide a useful backdrop for assessing whether forced GCM simulations, such as those by M a y (2004), K u m a r et al. (2006), among others, provide plausible scenarios for changes i n extreme rainfall i n the twenty-first century.

This paper presents an exploratory, spatially dis tributed analysis of the nature of monotonic trends i n selected statistics of daily rainfall across India. T h e re search presented differs from recent work o n the issue ( G o s w a m i et al. 2006; Guhathakurta and Rajeevan 2008; Joshi and Rajeevan 2006; Rajeevan et al. 2008; A l e x a n d e r et al. 2006; K l e i n T a n k et al. 2006; K u m a r et al. 2006; M a y 2004) i n the specific statistics (frequency and intensity) of extremes considered, i n the use o f a Corresponding author address: Chandra Kiran B. Krishnamurthy, nonparametric monotonie trend analysis (instead o f Columbia University. 918 S.W. Mudd Building, Mail Code 4711, a linear trend analysis, which is nonrobust to outliers, a 500 W. 120th St., New York,NY10027. concern i n analyzing data on extremes), and i n analyzing E-mail: [email protected] DOI: 10.1175/2009JCLI2896.1 © 2009 American Meteorological Society

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the complete spatially distributed dataset instead of an aggregate region. Further, we use methods for field sig nificance analysis of spatial trends in each statistic and also document the concordance of trends across vari ables. Trends i n the frequency with which daily rainfall exceeds selected thresholds, as well as i n the intensity (magnitude of such rainfall events) are considered at each grid cell over India. The rainfall amount considered to define the exceedance events corresponds to fixed per centiles of the long-term rainfall data at that grid cell; hence, the threshold magnitude varies from grid cell to grid cell. Thus, changes i n the local climatology of extremes, rather than the rate of occurrence of a fixed extreme magnitude across a region or even the entire country, are explored. Further, analyzing trends i n frequency and intensity separately is of interest since it is possible that the number of extreme events could increase without a correspond ing increase in the intensity of each event (Trenberth 1999), and each measure provides information regarding different aspects of extreme rainfall. F o r instance, rainfallindexed insurance is being introduced by several organi zations in India (Gine et al. 2007) and the determination of a fair premium, and the associated payout structure, requires an assessment of whether the upper tail of the probability distribution of daily rainfall is changing at the specific location where contracts are likely to be written. The need to inform these and similar applications moti vates our spatially distributed analysis of trends in the exceedance of specific percentiles of the local distribution of daily rainfall. In the monsoonal setting (Indian or A s i a n monsoon), there have been a few studies focused exclusively on trends in extreme rainfall and most of these have been based on greenhouse-gas-forced model-based scenarios of the IPCC for the twenty-first century (Lal et al. 2000; Bhaskaran and M i t c h e l l 1998; M a y 2004; K u m a r et al. 2006). K e e p i n g i n m i n d the biases i n the models (indi cated i n K u m a r et al. 2006), we note that most models appear to predict enhanced summer monsoonal pre cipitation over parts of northwestern India, while pre dicting little or no change over much of peninsular India ( K u m a r et al. 2006). Climate-model-based studies ap pear to indicate an increase in the geographic extent of intense events but not necessarily an intensification of extreme events i n areas already subject to high rainfall [which tend to be along the southwestern coast or the northeastern sub-Himalayan region ( K u m a r et al. 2006)]. M o d e l results also indicate intensification of rainfall i n most of India except parts of central and northeastern India ( M a y 2004), with the most intense (maximum 24-h rainfall) rainfall events predicted to occur over north eastern and northwestern India.

The study by G o s w a m i et al. (2006), using the same gridded dataset as here, reports an increasing trend i n the frequency of extreme precipitation events, defined as events exceeding the thresholds of 100 and 150 m m , using pooled data from all grid cells over the central Indian region (the so-called monsoon belt), and also indicates an increase i n the intensity of precipitation, as measured by the raw values of the 99.5th and 99.75th percentile of the rainfall distribution, over the same region. Joshi and Rajeevan (2006) use station data (about 199 stations from 1901 to 2000) for India to carry out a linear, parametric trend analysis on various measures of extremes. They find increasing trends for certain regions (west coast and northwestern India) as well as an i n crease (as in G o s w a m i et al. 2006) i n the contribution of heaviest rains to total rainfall. Finally, Rajeevan et al. (2008), using a longer station-level dataset (1901-2004), carry out an analysis very similar to G o s w a m i et al., over a slightly different region, and find increasing trends (after accounting for interdecadal variations i n the ex treme events) i n both heavy and very heavy rainfall events (as defined in G o s w a m i et al. 2006). T h e y also make a preliminary attempt at linking such trends to ocean surface temperatures. a.

Data

This study utilizes a recently available gridded daily dataset for India (Rajeevan et al. 2006), consisting of 1300 grid cells, each 1° latitude × 1° longitude, for 53 years (1951-2003), available from the I M D . O f these 1300 grids, 357 grids covering all of India's land area were used for the analysis. This is the same dataset from which G o s w a m i et al. (2006) draw their subset for analysis. b. Definition

of statistics of extremes

W e consider two measures of extremes, frequency and intensity, defined, respectively, as the number of days with rainfall events (each year) exceeding a threshold and the average daily rainfall (for each year) on the days on which rainfall exceeds the specific threshold. A threshold is defined in terms of a fixed percentile (two were considered: the 90th and the 99th) of the daily rainfall series at the grid cell, considering only days with nonzero rainfall. A s a result, the threshold magnitude varies from grid cell to grid cell (but not year to year). A time series of frequency at each grid cell is computed as

where t is the year, j the grid box, P the rain on day i i n year t at grid j, and P is the rainfall threshold for grid j; itj

*

j

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KRISHNAMURTHY ET AL.

FIG. 1. Contours of exceedance thresholds of daily rainfall (mm) at each grid. The boxed area indicates the region considered in Goswami et al. (2006).

The primary analyses were carried out separately for F is an indicator function that takes the value 1ifthe data for the monsoon season, June-September, and for argument is true and 0 otherwise. the rest of the year. T h e monsoon season results are Correspondingly, the intensity time series is derived reported here. as (following the same notation) c. Trend

F o r each grid cell, the number of nonzero precipita tion events during each year was identified and the 90th (99th) percentile of this series estimated. T h e median of these 90th (99th) percentile values across all years was then selected to be the threshold for that particular grid cell. T h e spatially varying climatology of extreme rain fall across India is thus addressed (see also Joshi and Rajeevan 2006, p. 6). W e feel that this procedure better represents the spatial aspects of the monsoon process than a threshold fixed across grids, since the monsoon rainfall varies substantially across India, and we are interested i n how the spatial pattern of extreme rainfall may have changed across the country. This is evident from F i g . 1, which illustrates that the spatial pattern of the thresholds are very similar to the monsoonal precipitation patterns, with the largest thresholds obtained at the southwest ern, western coast, and the northeastern region.

analysis

T h e M a n n - K e n d a l l ( M K ) test is used for the detec tion of monotonic trends in the derived frequency and intensity data for each grid cell. An estimate of the Sen slope, a robust estimate of the monotonic trend, is also computed, along with its significance level. The M K test is a rank-based test, with no assumptions as to the underlying probability distribution of data (Helsel and H i r s c h 1992, 326-327). T h e test statistic, computed based on pairwise comparison between the values of a series, is asymptotically normally distributed, indepen dent of the distribution of the original series. A robust estimate of the magnitude of the slope of the trend is estimated using the method of Sen, as the median of pairwise slopes between elements of the series ( Y u e et al. 2002, 16-17). F o r each grid cell, and separately for the frequency and the intensity data, we test (at the 10% significance level) (i) the null hypothesis of no trend, (ii) the null hypothesis o f n o increasing trend, and (iii) the null hypothesis of no decreasing trend. Recognizing that a certain number of rejections of the null hypothesis are to be expected, given the large number of tests conducted.

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F I G . 2. Spatial distribution of grids for which the null of no trend is rejectedbytheMKtest(one-sidedatthe10% significance level): blue indicates decreasing and brown indicates increasing trends: exceedance of the 90th and 99th percentile of daily rainfall is considered. The boxed area indicates the region considered in Goswami et al. (2006).

we construct a field significance test (described i n the next section) to assess whether the outcomes of the significance tests at the grid level may be consistent with what is expected purely by chance. H e r e , we examine the general features of the trends revealed by the MK test. Figure 2 provides the spatial distribution of the trends for grids where the null hypothesis of no monotonic trend is rejected at the 10% significance level, while Table 1 provides a tabulation of the number of such grids. F o r exceedances of the 90th percentile, the number of decreasing trends in frequency dominates the number of increasing trends. This observation runs counter to the

assessments reported in the literature, where increasing trends i n extremes are the focus. F o r instance, G o s w a m i et al. (2006) and K u m a r et al. (2006) find only increas ing trends (in the first case over a restricted subset of the d o m a i n investigated here) with a fixed threshold of rainfall applied. Joshi and Rajeevan (2006), using thresholds varying with station, is the only study to re port decreasing trends (at a few stations). N o t e from Table 1 that the number of increasing trends in intensity is higher than decreasing trends at the same threshold, which suggests that, when exceedance of the 90th per centile of grid rainfall occur, the amount of rain has been increasing—an observation likely to support the

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TABLE 1. Distribution of grids with statistically significant (at the α = 10% significance level) trends (357 grid cells in total). l

Number of grids with trend

90th percentile threshold Frequency Intensity 99th percentile threshold Frequency Intensity

Increasing

Decreasing

25 44

61 27

45 42

30 25

direction of trends reported in G o s w a m i et al. (2006) (with a fixed rainfall threshold) and in Joshi and Rajeevan (2006) (with a spatially varying threshold). A perusal of the trends in frequency and intensity of exceedance of the 99th percentile threshold supports such a speculation, given the dominance of increasing trends in both frequency and intensity at this threshold. However, contrary to much of the literature, a fair number of decreasing trends are noted in our analyses. F r o m the figures it is clear that, while the details vary by threshold and metric (frequency and intensity), increasing trends dominate i n the coastal regions and i n the eastern re gion (west of Bangladesh), while decreasing trends ap pear to be more prevalent i n the northern, central, and northeastern parts of India. Indeed, from these figures, it is difficult to argue that there has been an increase i n the frequency and intensity o f extreme rainfall across India. The joint trends i n frequency and intensity are inves tigated next. The motivation is to investigate whether, as hypothesized i n Trenberth (1999), trends i n both fre quency and intensity increase or decrease jointly. T h e trends in frequency and intensity (in Figs. 3 and 4) that are deemed significant in the independent analyses agree completely for exceedances o f the 99th percentile threshold. F o r exceedances of the 90th percentile, de creasing trends i n frequency and intensity at the same location are much more prevalent than joint increasing trends i n these two metrics. It is remarkable that at the higher threshold, there is not a single grid cell with op posite directions of trends i n frequency and intensity, while at the lower threshold, grids with opposing trends are evident only i n the monsoon belt. At the lower threshold, there are not very many grid cells for which trends i n both frequency and intensity are significant. Most grids with trends significant i n both are located i n the eastern part of the country. G i v e n the spatial structure of the Indian monsoon, it is pertinent to ask if a similar (or some) structure is evident in the trends as well. To investigate this aspect, we plot the contours of the trends calculated at each grid

FIG. 3. Assessment of consistency in significant trends in fre quency and intensity (at the 90th percentile threshold): cyan indi cates trends in both frequency and intensity decreasing, brown indicates trends in both frequency and intensity increasing, and blue indicates trends in frequency increasing and intensity decreasing. Only grids in which trends in both frequency and intensity were statistically significant (at the 10% level) are considered. The boxed area indicates the region considered in Goswami et al. (2006).

point and note that, if there were some spatial structure in the trends, it would be evident i n the contour plots. However, a perusal of Figs. 5 and 6 indicates that there is no evident structure to the trends, of either sign. H a v i n g taken a broad look at the spatial distribution and direction of trends in the frequency and intensity of extreme rainfall across India, we next examine whether the number of statistically significant trends that appear

FIG. 4. As in Fig. 3 but at the 99th percentile threshold: blue indicates trends in both decreasing: brown indicates trends in both increasing.

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FIG. 5. Contours of the trend estimated by the Sen slope for frequency of exceedance at each of the grids. Grids with statistically significant trends (at the 10% level of significance) are marked with an asterisk and 0. The boxed area indicates the region considered in Goswami et al. (2006).

to be different from zero at the 10% significance level could occur purely by chance, i n an analysis o f the spatially distributed dataset used here. d. Field significance

test

at the α % significance level (global o r across the domain). A one-sided test is used, to test whether the propor tion of grids with significant trends p is greater than the (global) significance level α , as below: f

1

f

T h e question addressed i n this section is whether the number o f increasing o r decreasing trends deemed significant at the gridcell level analysis c o u l d occur purely by chance, taking into account the possibility that the rainfall data, a n d hence the trends, have a n underlying spatial structure. T h e answer to this ques tion depends on the specific area or d o m a i n considered [all o f India or the core monsoon region, as identified i n G o s w a m i et al. (2006) a n d indicated as a box i n all figures]. Results for the all-India data are presented first and those for the smaller, core monsoon region are discussed next. T h e so-called field significance test ( L i v e z e y a n d C h e n 1983) has been typically used to address the question posed i n this section. T h e n u l l hypothesis of the test is that the number n out o f N total grid cells e x h i b i t i n g a trend at the α% level o f significance (local or at each grid cell) is not inconsistent w i t h the value expected by chance, considering the potential for spatial c o r r e l a t i o n across the i n d i v i d u a l time series analyzed for trends. T h e n u l l hypothesis is rejected if n is larger than the number expected by chance

H :p 0

= α

f

vs H :p>α . a

f

The test statistic

is distributed N(0, 1) under the null. In most applications, the validity of the field signifi cance test is compromised by the finiteness of the dataset used and by the spatial and/or temporal correlation between the series used (Livezey and C h e n 1983; E l m o r e et al. 2006; W i l k s 1997). W e outline a procedure that addresses the spatial dependence of data. Spatial correlation reduces the degree-of-freedom of the test;

l

1

Note that the local significance level α is always taken to be 10%, while the global significance level α is either 10% or 5% depending on whether thefieldsignificance test pertains to both increasing and decreasing (significant) trends or only increasing or decreasing trends. l

f

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FIG. 6. As in Fig. 5 but tor intensity.

that is, there are less than N individual realizations (of the test statistic or phenomenon; in this case, frequency and intensity) i n a field of size N. L i v e z e y and C h e n (1983) estimate the effective number of realizations, n < N, by a M o n t e C a r l o procedure involving gener ating the sampling distribution of n under the null (of field nonsignificance), obtaining a desired percentile (say, the 5th) of this distribution, and comparing it to the m i n i m u m number of effective degree of freedom for the significance of the field, n . T h e null hypothesis is rejected if n > n . 0

This approach preserves the correlation structure across space but not across time. Serial correlation across years i n each grid cell was not found to be significant. F o r each of the 1000 samples generated,theMKtestwasrepeatedfor each grid and for each sample. This leads to 1000 samples at each grid cell with a binary determination of trend sig nificance at the α % level. The proportion of grid cells for which significant trends at the α % level were found was calculated for each of the 1000 samples to obtain 1000 l

l

realizations of the proportion of grids, p, exhibiting trends

at the local significance level. This provides an estimate of An alternative is to generate the sampling distribution the sampling distribution of the test statistic under the of the test statistic under the null hypothesis, keeping null hypothesis that the number of trends identified as intact the spatial structure of the dataset under consid significant at the α% level, across the domain, is consis eration. T h e advantages of this approach include sam tent with the number expected by chance. This compu pling the spatial correlation structure without formally tation was done separately for increasing and decreasing specifying it (Wilks 1997). significant trends i n frequency and intensity, leading to six 0

l

T h e bootstrap is a nonparametric method that sam ples, with replacement, from the original data. It is ap plied here by resampling the spatial field associated with each year, which preserves the spatial structure but randomizes the temporal structure. T h e bootstrapping procedure for the field significance test was carried out by first generating 1000 random samples of 53 numbers, each from 1 to 53 (with replacement). E a c h of these 1000 samples is then treated as a realization of a time index corresponding to 53 years of data, with the fre quency and intensity spatial fields then sampled for each of these generated years.

different tests for each exceedance threshold. The pro cedure and results are summarized below. (i) M a n n - K e n d a l l trend test: C a r r y out the MK test; obtain the Sen slope and a count of the number of grids at which the null (of trend nonsignificance) was rejected (at the 10% level); compute the test statistic, denoted t . This step is carried out for each of three types of trends (trends in both d i rections, increasing trends and decreasing trends only), and steps (ii) and (iii) are then repeated separately for each of these three types of trends. sample

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TABLE 2. Bootstrap test results [note i) t: raw statistic;t*:critical value—the (1 - α ) quantile of the bootstrap distribution ii) α for increasing and decreasing trends is 0.05, while for all significant grids it is 0.1 and iii) null offieldnonsignificance (p = α ) is rejected if t > t*]. f

f

f

Frequency Trend 90th percentile threshold Both increasing and decreasing Increasing only Decreasing only 99th percentile threshold Both increasing and decreasing Increasing only Decreasing only

Intensity

t*

t

Null

t*

t

Null

-0.078 0.025 -0.073

0.141 -0.03 0.071

Reject Do not Reject

-0.042 -0.039 0.008

0.099 0.023 -0.024

Reject Reject Do not

-0.056 -0.039 0

0.11 0.026 -0.016


-0.034 -0.031 0.014

0.088 0.018 -0.03


of these events is increasing. A contour plot o f the slopes of frequency and intensity provides a smoother representation o f the nature o f these trends (Figs. 5 and 6).

(ii) F i e l d significance test: • R a n d o m l y sample, with replacement from the data, to obtain 1000 copies of the data matrix while retaining the spatial structure.

N o w consider the results over the region considered by Goswami et al. (2006), the main study with a similar analysis and dataset. Recall that G o s w a m i et al. define extremes over a homogeneous region and use the number of days of rainfall above 100 and 150 m m and the intensity of rainfall for a fixed percentile (99.5th and 99.75th) as measures ofvector extremes. They -t ).Sortthis andobtain itsreport an increase i n the frequency of extreme rainfall events as well as an increase •TestT =int -the αaginstT*(recalth a intensity of extreme rainfall. Carrying out the field significance test outlined i n the preceding section over one-sided test is e m p l o y e d ) and reject the null their domain, we find that the broad conclusions from the hypothesis that the number of significant trends is national analysis are essentially unchanged (Tables 3 what w o u l d be expected by chance i f T > T*. and 4); that is, while increasing trends do exist, they are (iii) Repeat the analysis for different thresholds. more predominant in the southwestern coast and north T h e results o f the bootstrap procedure are summa eastern regions, with decreasing trends being more promi rized i n T a b l e 2. First, if we consider the total number nent in the central regions. of trends (of either sign), we observe that the null hy Joshi and Rajeevan (2006), using a different dataset, pothesis is rejected for all tests. N e x t , i f we consider find increasing trends (using somewhat different measures increasing trends only i n the case of frequency of ex of extremes) i n very similar regions; they also report ceedance of the 90th percentile is the null hypothesis negative trends (at only two stations). not rejected. Changes i n intensity indicate an increasing G o s w a m i et al. (2006) also performed a split sample trend at both thresholds. T h e number of decreasing analysis, splitting the data into two parts, pre- and posttrends passes the significance test only for frequency at 1981, and find an increasing trend i n the post-1981 the 90th percentile. Thus, i n summary, the hypothesis that overall there is an increasing trend in the frequency and intensity of extreme rainfall appears to have sup TABLE 3. Distribution of grids with statistically significant (at port with the caveat that, at the 90th percentile, the α = 10% significance level) trends in the region defined by Goswami et al. (2006) (74 grid cells in total). frequency of exceedance appears to be decreasing i n the central and northern regions, while the intensity

• O b t a i n 1000 realizations of the proportion of the grid cells, p, for which the hypothesis of no trend is rejected and the vector (of size 1000) of test statistics (denoted t ). • Construct the bootstrap estimate o f the sampling distribution o f the test statistic T = (t 100(1 - α ) percentile (denoted T*). bootstrap

bootstrap

bootstrap

th

sample

2

f

sample

f

3

l

Number of grids with slopes

90th percentile threshold This is known as the "percentile method" of bootstrap-based Frequency hypothesis testing (Davison and Hinkley 1997, 201-203). Intensity We note that this approach differs from the conventional one, 99th percentile threshold involvingtestingT vsα;theapproachadoptedhereismore Frequency efficient than the conventional one (Hall and Wilson 1991; Wilks Intensity 1997).

Increasing

Decreasing

7 17

9 2

13 12

4 4

2

3

bootstrap

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TABLE 4. Bootstrap test results for slopes in region defined by Goswami et al. (2006) [note i) t: raw statistic; t*: critical value—the (1 - α ) quantile of the bootstrap distribution ii) α for increasing and decreasing trends is 0.05, while for all significant grids, it is 0.1 and iii) null of field nonsignificance (p = α ) is rejected if t > t*]. f

f

f

Intensity

Frequency Trend 90th percentile threshold Both increasing and decreasing Increasing only Decreasing only 99th percentile threshold Both increasing and decreasing Increasing only Decreasing only

t*

t

Null

t*

t

Null

-0.014 0.041 0

0.103 -0.019 0.022

Reject Do not Reject

-0.068 -0.122 0.068

0.143 0.116 -0.073


-0.041 -0.054 0.041

0.116 0.062 -0.046


-0.027 -0.054 0.041

0.103 0.049 -0.046


sample. W e repeated o u r analysis for the same two subperiods. T h e results of this analysis indicate that the conclusions obtained using the full sample are unaltered, unlike G o s w a m i et al. who find a increasing trend only i n the post-1981 sample. T h e importance o f the spatially distributed analysis performed here is that, if the spatial differences noted represent nonhomogeneous aspects of the monsoon, then the spatial patterns identified i n the trends would potentially help inform mechanism iden tification and m o d e l performance evaluation.

H o w e v e r , there is considerable spatial variation as to the direction of change, and the spatial continuity of trends deemed statistically significant is weak. This is not unexpected since threshold crossings are a random process and the assessment o f significance is also a threshold process. A visual examination of the spatial variation i n the trends i n frequency and intensity of extreme rainfall suggests that the north a n d central sections of the Indian Subcontinent have experienced a generally decreasing trend i n the frequency and inten sity of extremes, while the coastal regions in peninsular India and the region immediately west of Bangladesh have experienced increasing trends.

K u m a r et al. (2006) find significant increases i n i n tense precipitation i n much of western, northwestern, and especially the southwestern regions. T h e results of E v e n i n central India, which was analyzed i n aggre the present analysis indicate trends mostly i n parts of gate by a previous study, there is some heterogeneity in the southwestern coastal regions, similar to the results the direction of the trends, and the larger-scale analysis of K u m a r et al., as well as i n the eastern and central performed here helps clarify the spatial structure of the regions. M a y (2004) reports increases over much of the changes i n the region studied i n G o s w a m i et al. (2006). Indian peninsula, while the coarse spatial resolution of the m o d e l used does not provide detail over smaller W e do not attribute the trends observed to anthro regions of India. Further, o u r results that decreasing pogenic climate change or to interdecadal climate vari trends are likely i n many areas are i n concurrence ability, which may be of natural origin. Rather, we offer with M a y (2004), who also finds similar decreases (in the results of this analysis as a benchmark to the climate the scale and/or shape parameters of the gamma o r the community to consider more detailed studies o f the Generalised Pareto (GPA) distributions, which are fit to spatial structure o f changes i n the Indian monsoon the rainfall data) for a small number o f regions. H o w mechanisms so that a better informed attribution of ever, the spatial coarseness o f the m o d e l prevents a change can be determined. closer spatial comparison of the results. Generally, it is k n o w n that tropical depressions that form i n the B a y of B e n g a l and then propagate westward or northward play a key role i n extreme rainfall. These 2. Discussion and conclusions are associated with a mix o f barotropic and baroclinic instabilities theirininteraction with the mean m o n Anearlier examinationand oftrends extremesofIn soonal flow ( G a d g i l 2003). W e suspect that the details of dian monsoon rainfall was developed further in this these interactions may be associated with the indicated work. T h e analysis considered the spatial structure o f changes i n the spatial structure o f the trends and, nat changes i n the extremes across the country rather than urally, with the trends themselves. A recent study by over a b o x (homogenous region) i n central India. Guhathakurta and Rajeevan (2008) notes a significant B r o a d l y speaking, there is support for the hypothesis decreasing trend i n the frequency of depressions and that the frequency and intensity of extreme rainfall over storms over the B a y of Bengal, lending support to our India m a y be increasing over the previous 53 years.

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conjecture. M o d e l - b a s e d studies a n d detailed analysis of i n d i v i d u a l extreme events are necessary to develop this i n t u i t i o n and are being pursued. T h e design of our study was somewhat different from p r i o r w o r k . First, we considered changes i n the c l i m a tology of extremes for each spatial location, rather than the frequency a n d intensity o f exceedance o f a fixed threshold, which is more meaningful for an analysis of the larger spatial scale considered. Second, instead o f considering linear trends, we considered the more gen eral case of m o n o t o n i c trends (this w o u l d include, e.g., a step change i n the process at some time o r an expo nential o r logarithmic trend) and assessed the evidence for such a trend using robust, nonparametric methods. T h e field significance test was a p p l i e d both nationally and regionally and essentially confirms that the number of cases for w h i c h the null hypothesis o f n o trend was rejected was statistically different from that obtained purely by chance (at the relevant level of significance). T h u s , our study lends credibility to previous assess ments that report increasing trends i n frequency a n d intensity o f extreme rainfall over India, while identify ing areas where there is a systematic departure from previous assessments. T h e issue o f how these trends

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TITLE: Changing Frequency and Intensity of Rainfall Extremes over India from 1951 to 2003 SOURCE: J Clim 22 no18 S 15 2009 The magazine publisher is the copyright holder of this article and it is reproduced with permission. Further reproduction of this article in violation of the copyright is prohibited.